Is unix a graphical user interface?

Answer 1

No, its an operation system.

But many GUIs have been written to run on unix.

Unix is not a graphical user interface (GUI). It is an operating system that originally did not have a graphic interface and still does not have a GUI interface as part of the system. The standard user interface in UNIX is a command line as in a terminal session, similar to a windows command line interface.

Various graphic user interfaces are available for the unix and linux platform. Nearly all are based on the X Windows System (or X or X11 for version 11). X is a system for describing via API (program calls) and tables all the parts of a GUI including window attributes, position, boundaries, menus, mouse/pointer and input support. Nearly all unix/linux implementations as well as some other systems use X to create the windowing environment from the simple TWM (Tab Windows Manager) to DecWindows, Motif, CDE (Common Desktop Environment), to Gnome, KDE, xfc, and many more.

It wasn't just a GUI environment for a computer. It was a client/server environment that allowed remote control of a machine from elsewhere on a network or the internet. The commands to start the windowing environment on your machine also allowed you to specify that all the graphic display output generated on your machine from your session (the client) should be sent to another machine running an X windows Server.